On the Convergence to a Global Solution of Shuffling-Type Gradient Algorithms

• URL: http://arxiv.org/abs/2206.05869v2
• Date: Thu, 26 Oct 2023 02:56:16 GMT
• Title: On the Convergence to a Global Solution of Shuffling-Type Gradient Algorithms
• Authors: Lam M. Nguyen, Trang H. Tran
• Abstract summary: gradient descent (SGD) algorithm is the method of choice in many machine learning tasks. In this paper, we show that SGD has achieved the desired computational general complexity as convex setting.
• Score: 18.663264755108703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which matches the mainstream practical heuristics. We show the convergence to a global solution of shuffling SGD for a class of non-convex functions under over-parameterized settings. Our analysis employs more relaxed non-convex assumptions than previous literature. Nevertheless, we maintain the desired computational complexity as shuffling SGD has achieved in the general convex setting.

Related papers

• Using Stochastic Gradient Descent to Smooth Nonconvex Functions: Analysis of Implicit Graduated Optimization [0.6906005491572401]
  We show that noise in batch descent gradient (SGD) has the effect of smoothing objective function. We analyze a new graduated optimization algorithm that varies the degree of smoothing by learning rate and batch size.
  arXiv  Detail & Related papers  (2023-11-15T07:27:40Z)
• Stability and Generalization of the Decentralized Stochastic Gradient Descent Ascent Algorithm [80.94861441583275]
  We investigate the complexity of the generalization bound of the decentralized gradient descent (D-SGDA) algorithm. Our results analyze the impact of different top factors on the generalization of D-SGDA. We also balance it with the generalization to obtain the optimal convex-concave setting.
  arXiv  Detail & Related papers  (2023-10-31T11:27:01Z)
• Accelerated stochastic approximation with state-dependent noise [7.4648480208501455]
  We consider a class of smooth convex optimization problems under general assumptions on the quadratic noise in the gradient observation. Such problems naturally arise in a variety of applications, in particular, in the well-known generalized linear regression problem in statistics. We show that both SAGD and SGE, under appropriate conditions, achieve the optimal convergence rate.
  arXiv  Detail & Related papers  (2023-07-04T06:06:10Z)
• A framework for bilevel optimization that enables stochastic and global variance reduction algorithms [17.12280360174073]
  Bilevel optimization is a problem of minimizing a value function which involves the arg-minimum of another function. We introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has $O(frac1T)$ convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption.
  arXiv  Detail & Related papers  (2022-01-31T18:17:25Z)
• The Benefits of Implicit Regularization from SGD in Least Squares Problems [116.85246178212616]
  gradient descent (SGD) exhibits strong algorithmic regularization effects in practice. We make comparisons of the implicit regularization afforded by (unregularized) average SGD with the explicit regularization of ridge regression.
  arXiv  Detail & Related papers  (2021-08-10T09:56:47Z)
• Distributed stochastic optimization with large delays [59.95552973784946]
  One of the most widely used methods for solving large-scale optimization problems is distributed asynchronous gradient descent (DASGD) We show that DASGD converges to a global optimal implementation model under same delay assumptions.
  arXiv  Detail & Related papers  (2021-07-06T21:59:49Z)
• Practical Precoding via Asynchronous Stochastic Successive Convex Approximation [8.808993671472349]
  We consider optimization of a smooth non-studied loss function with a convex non-smooth regularizer. In this work, we take a closer look at the SCA algorithm and develop its asynchronous variant for resource allocation in wireless networks.
  arXiv  Detail & Related papers  (2020-10-03T13:53:30Z)
• Balancing Rates and Variance via Adaptive Batch-Size for Stochastic Optimization Problems [120.21685755278509]
  In this work, we seek to balance the fact that attenuating step-size is required for exact convergence with the fact that constant step-size learns faster in time up to an error. Rather than fixing the minibatch the step-size at the outset, we propose to allow parameters to evolve adaptively.
  arXiv  Detail & Related papers  (2020-07-02T16:02:02Z)
• An adaptive stochastic gradient-free approach for high-dimensional blackbox optimization [0.0]
  We propose an adaptive gradient-free (ASGF) approach for high-dimensional non-smoothing problems. We illustrate the performance of this method on benchmark global problems and learning tasks.
  arXiv  Detail & Related papers  (2020-06-18T22:47:58Z)
• Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses [52.039438701530905]
  We provide sharp upper and lower bounds for several forms of gradient descent (SGD) on arbitrary Lipschitz nonsmooth convex losses. Our bounds allow us to derive a new algorithm for differentially private nonsmooth convex optimization with optimal excess population risk.
  arXiv  Detail & Related papers  (2020-06-12T02:45:21Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.